$J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 6x + 8$ and $ JT = 4x + 22$ Find $CT$.
A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {6x + 8} = {4x + 22}$ Solve for $x$ $ 2x = 14$ $ x = 7$ Substitute $7$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 6({7}) + 8$ $ JT = 4({7}) + 22$ $ CJ = 42 + 8$ $ JT = 28 + 22$ $ CJ = 50$ $ JT = 50$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {50} + {50}$ $ CT = 100$